"Normal" is a hard word to describe when it comes to temps of a trans. A few different factors help with that,
1. Is it a factory installed(within the radiator)
2. is it a factory installed aux cooler(outside of radiator)
3. Aftermarket installed(outside of radiator)
4. Aftermarket installed(in series with OEM cooler)
Typically, if it is #1. It "should" be around the same temp or a little cooler then the vehicle, ~200* or so. Any of the others are a toss up really.
I know I have seen them run as cool as 110* with #3 and 4. And as warm as 225* while towing.
I have a 28,000 GVWR rated #4 installed on my 97 Silverado and I see temps around 130* w/o a load, and 165* with a load, depending on whats tagging behind. And I always tow in 3rd, never OD.
If you have access to a infrared temp gun, tag the bottom of the pan after you have been driving for a while and see what it is. Not gonna be exact but youll get a close idea. I have a gauge installed with the sender in the pan side to get a more accurate temp reading.
Obviously the #1 killer of a transmission aside from poor maintenance is heat.
xcr440- Its not that it isnt shifting into OD. Its programmed settings not allowing to converter to lock up while in OD, thus creating more heat and waiting for all other parameters(ECT, o2 readings, speed and many others) to get where they need to be before it does. So its actually in a sense the vehicles way of heating up faster. Amazing what computers can do huh?
OP- The cooler works like a radiator, air to air cooling. The temp wont necessarily be as cool as "normal everyday driving" because it has a load on it that is not usually there in the above stated. It only gets cooled when the truck is moving yes, but as the fan is running while the vehicle is idle, it does cool it a bit that way too while parked. The fluid is always being cooled as long as it is running, just not as much as if you were driving. Heat is always being created though.
Dont always trust your factory gauge, use a temp gun or get an aux gauge if you are really cautious. There is a port on the left (driver) side of the 4L60E just above the range selector unit that you can put the sensor in if youd rather not drill a hole and weld a plate in on the pan. Wont be as accurate, but it will be fairly close.